Get Automated Technology for Verification and Analysis: 13th PDF

By Bernd Finkbeiner, Geguang Pu, Lijun Zhang

ISBN-10: 3319249525

ISBN-13: 9783319249520

ISBN-10: 3319249533

ISBN-13: 9783319249537

This ebook constitutes the court cases of the thirteenth foreign Symposium on automatic know-how for Verification and research, ATVA 2015, held in Shanghai, China, in October 2015.

The 27 revised papers awarded including 6 device papers during this quantity have been rigorously reviewed and chosen from ninety five submissions. They convey present learn on theoretical and functional features of automatic research, verification and synthesis by means of offering a world discussion board for interplay one of the researchers in academia and industry.

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Additional info for Automated Technology for Verification and Analysis: 13th International Symposium, ATVA 2015 Shanghai, China, October 12–15, 2015, Proceedings

Example text

Let (σ1 X1 (d1 : D) = ϕ1 (d1 )) . . e. for all 1 ≤ k ≤ m: ∃el : El . fl (dk , el ) ∧ Xl (gl (dk , el )) ϕk (dk ) = l∈Ik For variables X i , X j ranging over the set {Xk | 1 ≤ k ≤ m} and variables di , dj ranging over sort D, we define the SMT proposition occurs(X i , di , X j , dj ) as follows: occurs(X i , di , X j , dj ) ≡ (X i = Xk ) ∧ (X j = Xl ) ∧ ∃el : El fl (di , el ) ∧ (dj = gl (di , el )) 1≤k≤m l∈Ik The lemma below relates the existence of edges in the dependency space to the evaluation of the above-defined SMT proposition.

X n , dn ), viz. (X n , dn ), is equivalent to an element that occurred earlier in that sequence. We will use a variable k to indicate the starting point of the loop on the lasso. If such a lasso is ν-dominated, we have, according to Proposition 3, a proof graph. Encoding that the lasso is ν-dominated can be achieved by requiring that if (X n , dn ) = (X i , di ) for some i < m, then there is some (X j , dj ), for i ≤ j < n with an even rank and it is the lowest rank among the ranks on the loop.

To formalize our approach we first need to define such natural independence. Definition 5. Let N ∶= (P, T, F ) be a net. We define the natural independence relation ◊N ⊆ T × T on N as ● t ◊N t′ ⇔ ● t ∩ ● t′ = ∅ ∧ t● ∩ ● t′ = ∅ ∧ ● t ∩ t′ = ∅. In fact, one can prove that when N is safe, then ◊N is the notion of independence underlying the unfolding semantics of N . In other words, the equivalence classes of ≡◊N are in bijective correspondence with the configurations in the unfolding of N . The following result shows that the natural independence on the discovered occurrence net corresponds to the relation provided by the expert, when both we restrict to the set of co-enabled transitions.

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Automated Technology for Verification and Analysis: 13th International Symposium, ATVA 2015 Shanghai, China, October 12–15, 2015, Proceedings by Bernd Finkbeiner, Geguang Pu, Lijun Zhang

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